Image deconvolution is a process that attempts to reconstruct a true image from a degraded image, where the blurred image is a convolution of the true image and a blur kernel that may be spatially variant or invariant. Mathematically, a blurred image may be expressed as B=noise(I{circle around (×)}K), where I is the true image, K is the blur kernel, “noise” is a noise process, and B is the blurred image. A deconvolution process may be referred to as “non-blind deconvolution” where the blur kernel is known. On the other hand, where the blur kernel is not known, the deconvolution process may be referred to as “blind deconvolution.”
Image deconvolution finds utility in many different fields. For example, deconvolution may be used in scientific fields, such as astronomical and medical imaging, as well as in consumer electronics, such as digital cameras. For example, in consumer photography, image blurring may be difficult to avoid due to insufficient lighting, use of telephoto lenses, use of a small aperture for a wide depth of field, etc. Deconvolution may allow removal of blur from such images, and therefore produce a clearer image for viewing, printing, etc.
However, a deconvoluted image may contain unpleasant artifacts due to the ill-posedness of the deconvolution process, even if the kernel is known. Because the kernel may be bandlimited with a sharp frequency cutoff, there may be zero or near-zero values in its frequency response. At those frequencies the inverse of the kernel may have a very large magnitude, thereby causing excessive amplification of signal and noise. Two of the most prevalent resulting artifacts are ripple-like ringing around edges (i.e. transition regions) in the image, and amplified noise. Ringing artifacts are periodic overshoots and undershoots around an edge, which decay spatially away from the edge. It may be difficult to remove such artifacts after performing a deconvolution.